Gibbs energy defined

When equilibrium exists between the liquid and solid phases, the temperature is the freezing point Tf of the liquid. At equilibrium, the molar reaction Gibbs energy defined by ArG = J2iViiii is zero ... 

When M = the requited derivatives are given by equations 62 and 63. Moreover, the derivative on the left side of equation 64 defines the partial molar Gibbs energy, G. Therefore,... 

The chemical potential, plays a vital role in both phase and chemical reaction equiUbria. However, the chemical potential exhibits certain unfortunate characteristics which discourage its use in the solution of practical problems. The Gibbs energy, and hence is defined in relation to the internal energy and entropy, both primitive quantities for which absolute values are unknown. Moreover, p approaches negative infinity when either P or x approaches 2ero. While these characteristics do not preclude the use of chemical potentials, the appHcation of equiUbrium criteria is faciUtated by the introduction of a new quantity to take the place of p but which does not exhibit its less desirable characteristics. 

Analogous to the defining equation for the residual Gibbs energy is the definition of a partial molar residual Gibbs energy (eq. 161) ... 

A.ctivity Coefficients. Activity coefficients in Hquid mixtures are directiy related to the molar excess Gibbs energy of mixing, AG, which is defined as the difference in the molar Gibbs energy of mixing between the real and ideal mixtures. It is typically an assumed function. Various functional forms of AG give rise to many of the different activity coefficient models found in the Hterature (1—3,18). Typically, the Hquid-phase activity coefficient is a function of temperature and composition expHcit pressure dependence is rarely included. 

Other thermodynamic functions described above in that the change in free energy AG is determined solely by the initial and final states of the system. The maximum work, or maximum available energy, defined in terms of the Gibbs free energy G, which is now called the free enthalpy, is... 

The standard Gibbs free energy of reaction, AG°, is defined like the Gibbs free energy of reaction but in terms of the standard molar Gibbs energies of the reactants and products ... 

In the gas phase all sulfane molecules are relatively strong Bronsted acids. Their acidity is defined by the enthalpy or, alternatively, by the Gibbs energy of the following deprotonation reaction ... 

The derivation for equilibrium between a solution and a gaseous phase is based on the Henry law constant kiy defined on page 5. The standard Gibbs energy of the transfer of HC1 from a solution into water is... 

The key to understanding reaction equilibrium is the Gibbs free energy, ox free energy, defined as1-4 ... 

The change in Gibbs s free energy (defined, as stated, for a system at constant pressure and temperature) when a moles of A and b moles of B are converted into c moles of C and d moles of D is AG = cpc +dpD - apA - bpB, where p represent chemical potentials , i.e. free energy per mole of the substances, defined in terms of concentration of a component X as... 

The Gibbs energy of activation in Eq. (5.4) can be split into an enthalpy and an entropy term AGjx = AH x - T AS]x. Define two transfer coefficients... 

Define M/M+ = — AGsub — Im + AGg0l AGsub is the Gibbs energy of sublimation. 

The Helmholtz and Gibbs energies on the other hand involve constant temperature and volume and constant temperature and pressure, respectively. Most experiments are done at constant Tandp, and most simulations at constant Tand V. Thus, we have now defined two functions of great practical use. In a spontaneous process at constant p and T or constant p and V, the Gibbs or Helmholtz energies, respectively, of the system decrease. These are, however, only other measures of the second law and imply that the total entropy of the system and the surroundings increases. 

The Helmholtz and Gibbs energies are useful also in that they define the maximum work and the maximum non-expansion work a system can do, respectively. The combination of the Clausius inequality 7dS > dq and the first law of thermodynamics dU = dq + dw gives... 

In open systems consisting of several components the thermodynamic properties of each component depend on the overall composition in addition to T and p. Chemical thermodynamics in such systems relies on the partial molar properties of the components. The partial molar Gibbs energy at constantp, Tand rij (eq. 1.77) has been given a special name due to its great importance the chemical potential. The corresponding partial molar enthalpy, entropy and volume under the same conditions are defined as... 

Polynomial expressions are conveniently used to represent a condensed phase which is stable in the whole temperature range of interest and which does not undergo any structural, electronic or magnetic transformations. The Gibbs energy of a compound is in the CALPHAD approach represented relative to the elements in their defined standard state at 298.15 K as a power series in terms of temperature in the form of [16] ... 

Figure 3.8 The molar Gibbs energy of mixing of molten Fe-Ni at 1850 K using both the Raoultian (solid line) and Henrian (dashed line) standard states for Ni as defined in Figure 3.7. The Raoultian standard state is used for Fe. Data are taken from reference [3].

Figure 4.8 (a) Phase diagram of the binary system Y203 Mg0 at 1 bar defining the five temperatures for the Gibbs energy curves shown in (b) T (c) Ty, (d) Ty (e) Ty, (f) T. Thermodynamic data are taken from reference [6]. 

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